The height of a square-based pyramid is 21 cm and the length of the base is 20 cm.

1. How many triangular surfaces are there in a square-based pyramid? Write it.
2. Find the slant height of the pyramid.
3. What is the total cost of painting the total surface area of the pyramid at the rate of Rs. 5 per square cm? Find it.

40 tourists are coming from Switzerland to visit Mt. Everest. They planned to stay at Everest base camp for 4 days. For this purpose, they ordered some squared base pyramid tents in Nepal. A tent can hold 8 people and each person has 6 ft×3ft space on the ground with 48 cu.ft. of air to breathe. Find the total cost of all tents at the rate of Rs.560 per ft².

A metallic solid made up of a cone and a cylinder is given in the figure. The radii of the base of the cone and cylinder are equal. The height of the cylinder is 40cm, the height of the cone is 24cm and the radius of the base of the cone is 7cm.

1. If the radius of the base and the slant height of the cone are given then write the formula for finding the curved surface area of the cone.
2. Find the volume of the solid object.
3. Compare the volume of the cylindrical part and the volume of the conical part.

The length, breadth, and height of a rectangular room are 14 ft, 13 ft, and 10 ft respectively. There are two square windows with 3 feet edges and two doors of size 6ft × 3ft in the room.

1. How much does it cost to paint four walls and ceiling of the room excluding doors and windows at the rate of Rs. 36 per square foot? Find it.
2. How much the total cost will increase to paint on the same part if the cost of painting per square meter is increased by one-third of what it was before due to the increase in the market price? Find it.

The ratio of slant height and a side of base of square based pyramid is 5:6 and its total surface area is 1536 sq.cm.

1. Write the relation among base area (A), height(h), and volume(v) of the pyramid.
2. Compare the base area and the area of triangular surfaces.
3. Find the volume of the pyramid.

In the figure, cone is filled with ice-cream whose upper part is hemispherical. The slant height of the cone is 25cm and its radius is 7 cm.

1. Write the relation among the height (h), radius (r), and slant height (l) of the cone.
2. Find the total volume of ice-cream in conical and hemi spherical parts.
3. Compare the quantities of ice-cream in the conical and hemispherical parts.

The length, breadth and height of a rectangular room are 13ft, 12ft, and 10ft respectively. There are 2 windows of size 3ft×4ft and a door of size 3ft×6ft.

1. How much does it cost to paint four walls and celling excluding door and windows at the rate of Rs. 40 per square ft? Find it.
2. By how much will the total cost of painting the same parts of the room be increased if the rate of cost per square feet is increased by 25%? Find it.

A group of tourists planned to fix a pyramid-shaped tent at the Everest Base Camp as shown in the figure. The length of a side of its base is 12 ft and the area of triangular surfaces is 240 sq. ft.

1. Write the formula to find the area of triangular surfaces of a square-based pyramid.
2. Find the slant height of the tent.
3. If 64 cu. ft. of air is required for a tourist, how many tourists can be accommodated easily in the tent? Find it.

In the figure, a conical object with slant height 25 cm and a hemispherical object with radius of 7 cm is composed to make a solid object.

1. What type of triangle is formed when the vertical height of the cone is drawn in the given figure? Write it.
2. What will be the total cost to paint the solid at the rate of 25 paisa per square centimeter? Find it.
3. What is the volume of the solid object? Find it.

The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Tiles of length 25 cm, breadth 20 cm and height 5 mm are paved on the floor of the room.

1. How much cost of carpeting is required in the room at the rate of Rs. 250 per sq.m? Find it.
2. How many maximum numbers of tiles can be paved on the floor? Find it.

If the heights of two square-based pyramids are in the ratio of 2:3 and their volumes are in the ratio of 4:5. What is the ratio of their base area?

What is the mathematical relationship between the volume of a cone (Vco) and a cylinder (Vcy)?